Simulating Time Evolution with Fully Optimized Single-Qubit Gates on Parameterized Quantum Circuits

TL;DR

This paper introduces a comprehensive optimization method for single-qubit gates in parameterized quantum circuits, enhancing simulation of time evolution and extending to two-qubit gates with conservation constraints.

Contribution

It presents a fully optimized approach for single-qubit gates that improves simulation accuracy and extends to constrained two-qubit gates, generalizing existing methods.

Findings

Effective in finding ground states of Hamiltonians

Applicable to both real and imaginary time evolution

Balances simulation accuracy with hardware efficiency

Abstract

We propose a novel method to sequentially optimize arbitrary single-qubit gates in parameterized quantum circuits for simulating real and imaginary time evolution. The method utilizes full degrees of freedom of single-qubit gates and therefore can potentially obtain better performance. Specifically, it simultaneously optimizes both the axis and the angle of a single-qubit gate, while the known methods either optimize the angle with the axis fixed, or vice versa. It generalizes the known methods and utilizes sinusoidal cost functions parameterized by the axis and angle of rotation. Furthermore, we demonstrate how it can be extended to optimize a set of parameterized two-qubit gates with excitation-conservation constraints, which includes the Hop and the Reconfigurable Beam Splitter gates. We perform numerical experiments showing the power of the proposed method to find ground states of typical Hamiltonians with quantum imaginary time evolution using parameterized quantum circuits. In addition, we show the method can be applied to real time evolution and discuss the tradeoff between its simulation accuracy and hardware efficiency.